{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NNSRHYI77RPTUKX5XUEE6B5UZD","short_pith_number":"pith:NNSRHYI7","canonical_record":{"source":{"id":"1701.01762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-06T21:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"8c79aa2a3c22815b36838d6d6f1ed93826abd66108a5c5c88ae8fb6ba03636f1","abstract_canon_sha256":"e682a77b13a97995ea76dfb057e1133d7cd9f688e3d59be10d18bddf5f003698"},"schema_version":"1.0"},"canonical_sha256":"6b6513e11ffc5f3a2afdbd084f07b4c8fb05ab8ed4c0a6a67835af52f84fbe65","source":{"kind":"arxiv","id":"1701.01762","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01762","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01762v1","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01762","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"NNSRHYI77RPT","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NNSRHYI77RPTUKX5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NNSRHYI7","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NNSRHYI77RPTUKX5XUEE6B5UZD","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-06T21:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"8c79aa2a3c22815b36838d6d6f1ed93826abd66108a5c5c88ae8fb6ba03636f1","abstract_canon_sha256":"e682a77b13a97995ea76dfb057e1133d7cd9f688e3d59be10d18bddf5f003698"},"schema_version":"1.0"},"canonical_sha256":"6b6513e11ffc5f3a2afdbd084f07b4c8fb05ab8ed4c0a6a67835af52f84fbe65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:15.180807Z","signature_b64":"VhMmkLP28U9LMxanfiZzMK2LtoGBU4JbhO9K44VSDO0V6Qpzgq5AsJMp3ON22nGoyse5lmsVwNXUXDXMxI9vCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b6513e11ffc5f3a2afdbd084f07b4c8fb05ab8ed4c0a6a67835af52f84fbe65","last_reissued_at":"2026-05-18T00:53:15.180389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:15.180389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01762","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BgNtjwQitf1SJJlqS9mZLVaiZ9oQb0KVmPZNIWWRVDklCX/iEtFysxe/okQOOfC2BsBVCdi3XAWzcJDqxputBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:28:30.007510Z"},"content_sha256":"092d3c1d8b1f9919095aa9ed08075e524bfc6d1f58cb178c1bf0f796201235be","schema_version":"1.0","event_id":"sha256:092d3c1d8b1f9919095aa9ed08075e524bfc6d1f58cb178c1bf0f796201235be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NNSRHYI77RPTUKX5XUEE6B5UZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted relative trace formulae with a view towards unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eric Wambach, Jayce R. Getz","submitted_at":"2017-01-06T21:26:08Z","abstract_excerpt":"We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula of Jacquet and Lai. Certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven (including the relevant undamental lemma in the \"biquadratic case\"). Using recent work of Jacquet, Lapid and their collaborators and the Rankin-Selberg integral representation of the Asai $L$-function (obtained by Flicker using the theory of Jacquet, Piatetskii-Shapiro, and Shalika)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01762","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8+Pqg9IkeHl6E4xwAwIZ85FE+fjeD9jobOIR2xUNwmR/K4Tcn0oE2nEDoIVFmtGd0cTSKdtinLz6tNTfSjmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:28:30.007858Z"},"content_sha256":"df015ce18953db6b250cff13ec0fdfb3cdd1cd548c94e80fc3efd99aba5acd1f","schema_version":"1.0","event_id":"sha256:df015ce18953db6b250cff13ec0fdfb3cdd1cd548c94e80fc3efd99aba5acd1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNSRHYI77RPTUKX5XUEE6B5UZD/bundle.json","state_url":"https://pith.science/pith/NNSRHYI77RPTUKX5XUEE6B5UZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNSRHYI77RPTUKX5XUEE6B5UZD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T11:28:30Z","links":{"resolver":"https://pith.science/pith/NNSRHYI77RPTUKX5XUEE6B5UZD","bundle":"https://pith.science/pith/NNSRHYI77RPTUKX5XUEE6B5UZD/bundle.json","state":"https://pith.science/pith/NNSRHYI77RPTUKX5XUEE6B5UZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNSRHYI77RPTUKX5XUEE6B5UZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NNSRHYI77RPTUKX5XUEE6B5UZD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e682a77b13a97995ea76dfb057e1133d7cd9f688e3d59be10d18bddf5f003698","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-06T21:26:08Z","title_canon_sha256":"8c79aa2a3c22815b36838d6d6f1ed93826abd66108a5c5c88ae8fb6ba03636f1"},"schema_version":"1.0","source":{"id":"1701.01762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01762","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01762v1","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01762","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"NNSRHYI77RPT","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NNSRHYI77RPTUKX5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NNSRHYI7","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:df015ce18953db6b250cff13ec0fdfb3cdd1cd548c94e80fc3efd99aba5acd1f","target":"graph","created_at":"2026-05-18T00:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula of Jacquet and Lai. Certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven (including the relevant undamental lemma in the \"biquadratic case\"). Using recent work of Jacquet, Lapid and their collaborators and the Rankin-Selberg integral representation of the Asai $L$-function (obtained by Flicker using the theory of Jacquet, Piatetskii-Shapiro, and Shalika)","authors_text":"Eric Wambach, Jayce R. Getz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-06T21:26:08Z","title":"Twisted relative trace formulae with a view towards unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01762","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:092d3c1d8b1f9919095aa9ed08075e524bfc6d1f58cb178c1bf0f796201235be","target":"record","created_at":"2026-05-18T00:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e682a77b13a97995ea76dfb057e1133d7cd9f688e3d59be10d18bddf5f003698","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-06T21:26:08Z","title_canon_sha256":"8c79aa2a3c22815b36838d6d6f1ed93826abd66108a5c5c88ae8fb6ba03636f1"},"schema_version":"1.0","source":{"id":"1701.01762","kind":"arxiv","version":1}},"canonical_sha256":"6b6513e11ffc5f3a2afdbd084f07b4c8fb05ab8ed4c0a6a67835af52f84fbe65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b6513e11ffc5f3a2afdbd084f07b4c8fb05ab8ed4c0a6a67835af52f84fbe65","first_computed_at":"2026-05-18T00:53:15.180389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:15.180389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VhMmkLP28U9LMxanfiZzMK2LtoGBU4JbhO9K44VSDO0V6Qpzgq5AsJMp3ON22nGoyse5lmsVwNXUXDXMxI9vCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:15.180807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:092d3c1d8b1f9919095aa9ed08075e524bfc6d1f58cb178c1bf0f796201235be","sha256:df015ce18953db6b250cff13ec0fdfb3cdd1cd548c94e80fc3efd99aba5acd1f"],"state_sha256":"f72c93e80516f6cd36067ef72ff0ba79765ea29601efb25a3e4ef57ac73003aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"poZlCjCcRVwDVNuc5z3oUwPB1GI8DllHCN9qMG996z+mlZhpwcTvwXcsU8ZEuiq2Jc1ZFEeV6LF4LI7dolu+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:28:30.009766Z","bundle_sha256":"ce1005e352461aed0f86b6de4011fd1117a05417140c95825ab3f7d16b877cc1"}}